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U.S. Stock Market Returns after Extreme Up and Down Days

October 29, 2018 • Posted in Volatility Effects

What happens after extreme up days or extreme down days for the U.S. stock market? To investigate, we define extreme up or down days as those with daily returns at least X standard deviations above or below the mean (average) return over the past four years (the U.S. political cycle, about 1,000 trading days). This methodology allows identification of extreme days starting in January 1954. Focusing on three standard deviations, we then look at average returns and return variabilities over the next 63 trading days (three months). Using daily closes for the S&P 500 Index during January 1950 through late October 2018, we find that:

The following chart shows how the number of extreme days decreases at a decreasing rate as the threshold increases from one to 10 standard deviations from the average return over the prior four years. For a given threshold, numbers of extreme up and down days are comparable.

For subsequent analyses, we focus on a threshold of three standard deviations (3σ), with 114 extreme up days and 148 extreme down days. For a 3σ threshold, 66% of extreme up days and 66% of extreme down days occur when the S&P 500 Index is below its 200-day simple moving average.

How does the stock market behave on average after 3σ extreme events?

The next chart compares average daily S&P 500 Index returns during each of the 63 trading days after extreme up or down days. For reference, it also shows the average return for all days (0.033%) since January 1954. Ancillary statistics are:

  • After extreme up days, the average of average daily returns across the 63 trading days is 0.037%. Average variability (standard deviation of daily returns) during these 63-day intervals is 1.44%.
  • After extreme down days, the average of average daily returns across the 63 trading days is 0.052%. Average variability during these 63-day intervals is 1.57%.
  • Average standard deviation of daily returns across all 63-day intervals since January 1954 is 0.86%.

In other words, the stock market has typical (high) average daily returns and relatively high (high) variability during the three months after extreme up (down) days.

How do these average daily returns translate to cumulative behaviors?

The final chart compares average cumulative S&P 500 Index returns during the 63 trading days after extreme returns. For reference, it also shows the average cumulative return for all days since January 1954. Results show that, on average:

  • After the first two or three trading days, the above daily behaviors translate to cumulative underperformance over roughly the next month after both extreme up and down days.
  • Cumulative performance then reverts to typical or even outperformance by the end of three months. Results suggest that extreme down days may be better indications of end of market turbulence than extreme up days.

In summary, evidence indicates that the U.S. stock market tends to produce below-average returns with high volatility during the month after both extreme up and down days, but this underperformance then tends to revert during the following month.

Cautions regarding findings include:

  • Variability in stock market performance after extreme returns varies considerably across events, undermining confidence in average behaviors.
  • Other ways of defining extreme up and down days (such as for calibration look-back intervals other than four years) may produce different results.
  • Some of the extreme day observations involve overlapping future 63-day intervals. Such overlap can distort statistics.

For different perspectives, see “Trend Implications of Big Up and Down Days” and “Does a Long-Term Moving Average Indicator Predict Big Days?”.

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